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Electromagnetic wave scattering by many small particles
 PHYSICS LETTERS A 360 (2007) 735–741
, 2007
"... Scattering of electromagnetic waves by many small particles of arbitrary shapes is reduced rigorously to solving linear algebraic system of equations bypassing the usual usage of integral equations. The matrix elements of this linear algebraic system have physical meaning. They are expressed in term ..."
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Cited by 30 (26 self)
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Scattering of electromagnetic waves by many small particles of arbitrary shapes is reduced rigorously to solving linear algebraic system of equations bypassing the usual usage of integral equations. The matrix elements of this linear algebraic system have physical meaning. They are expressed in terms of the electric and magnetic polarizability tensors. Analytical formulas are given for calculation of these tensors with any desired accuracy for homogeneous bodies of arbitrary shapes. An idea to create a “smart” material by embedding many small particles in a given region is formulated.
Materials with a desired refraction coefficient can be made by embedding small particles
, 2007
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Preparing materials with a desired refraction coefficient
, 2008
"... A recipe is given for creating material with a desired refraction coefficient by embedding many small particles in a given material. To implement this recipe practically, some technological problems have to be solved. These problems are formulated. ..."
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Cited by 9 (8 self)
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A recipe is given for creating material with a desired refraction coefficient by embedding many small particles in a given material. To implement this recipe practically, some technological problems have to be solved. These problems are formulated.
NUMERICAL SOLUTION OF MANYBODY WAVE SCATTERING PROBLEM FOR SMALL PARTICLES
 DIPED2009 PROCEEDINGS
, 2009
"... A numerical approach to the problem of wave scattering by many small particles is developed under the assumptions ka << 1, d>> a, where a is the size of the particles and d is the distance between the neighboring particles. On the wavelength one may have many small particles. An impedanc ..."
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Cited by 6 (5 self)
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A numerical approach to the problem of wave scattering by many small particles is developed under the assumptions ka << 1, d>> a, where a is the size of the particles and d is the distance between the neighboring particles. On the wavelength one may have many small particles. An impedance boundary conditions are assumed on the boundaries of small particles. The results of numerical simulation show good agreement with the theory. They open a way to numerical simulation of the method for creating materials with a desired refraction coefficient.
Scattering by many small inhomogeneities and applications
"... Manybody quantummechanical scattering problem is solved asymptotically when the size of the scatterers (inhomogeneities) tends to zero and their number tends to infinity. A method is given for calculation of the number of small inhomogeneities per unit volume and their intensities such that embedd ..."
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Cited by 5 (5 self)
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Manybody quantummechanical scattering problem is solved asymptotically when the size of the scatterers (inhomogeneities) tends to zero and their number tends to infinity. A method is given for calculation of the number of small inhomogeneities per unit volume and their intensities such that embedding of these inhomogeneities in a bounded region results in creating a new system, described by a desired potential. The governing equation for this system is a nonrelativistic Schrödinger’s equation described by a desired potential. Similar ideas were developed by the author for acoustic and electromagnetic (EM) wave scattering problems.
Collocation method for solving some integral equations of estimation theory
, 2010
"... A class of integral equations Rh = f basic in estimation theory is introduced. The description of the range of the operator R is given. The operator R is a positive rational function of a selfadjoint elliptic operator L. This operator is defined in the whole space R r, it has a kernel R(x, y), and R ..."
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Cited by 3 (3 self)
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A class of integral equations Rh = f basic in estimation theory is introduced. The description of the range of the operator R is given. The operator R is a positive rational function of a selfadjoint elliptic operator L. This operator is defined in the whole space R r, it has a kernel R(x, y), and Rh: = R D R(x, y)h(y)dy, where D ⊂ Rr is a bounded domain with a sufficiently R smooth boundary S. Example of the equation of this type is